Substituted aluminum nitride for improved acoustic wave filters

ABSTRACT

A piezoelectric material comprises AlN doped with cations of one or more elements selected from the group consisting of: one of Sb, Ta, Nb, or Ge; Cr in combination with one or more of B, Sc, Y, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, or Yb; one of Nb and Ta in combination with one of Li, Mg, Ca, Ni, Co, and Zn; Ca in combination with one of Si, Ge, Ti, Zr, and Hf; Mg in combination with one of Si, Ge, and Ti; and one or more of Co, Sb, Ta, Nb, Si, or Ge in combination with one or more of Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, or Yb. The cations at least partially substitute for Al in the crystal structure of the piezoelectric material.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Patent application Ser. No. 62/529,742, titled “SUBSTITUTEDALUMINUM NITRIDE FOR IMPROVED ACOUSTIC WAVE FILTERS,” filed Jul. 7,2017, which is incorporated by reference herein in its entirety for allpurposes.

BACKGROUND

Aluminum Nitride (AlN) is a piezoelectric material that has been used inBulk Acoustic Wave (BAW) and Film Bulk Acoustic Resonator (FBAR) filtersoperating in the 1-5 GHz range. Larger group IIIA nitrides (e.g., GaNand InN) show a dramatically decreasing piezoelectric coefficient goingdown the series. The properties of AlN may be modified withsubstitutions for aluminum such as scandium. However, there is still aneed for improved electromechanical coupling, higher dielectricconstants, greater sound velocities and better temperature stability forthese materials which may lead to improved properties of the BAWfilters. As used herein, the term “BAW filter” includes FBAR filters.

Desirable properties in piezoelectric materials that may be used inacoustic wave filters include the following:

-   -   high speed of sound, for example, greater than 12,000 m/msec    -   good coupling constant, for example, greater than 5%    -   high dielectric constant to decrease size of device    -   stable materials system and crystal structure for deposition and        integration    -   wide band gap which provides for the material to be a good        insulator with low leakage

The relationship between various parameters of BAW filters and thematerial properties of the piezoelectric material utilized in suchfilters include the following:

-   -   Increased bandwidth=Increased coupling factor k²    -   Steep edges for filter=Increased quality factor Q    -   Filter thickness miniaturization=increased sound velocity        v=(c₃₃/ρ)^(1/2); c₃₃=elastic modulus, ρ=material density.    -   Filter miniaturization in x-y plane=Increased dielectric        constant    -   Low leakage current, Better insulator=Wide band gap    -   Filter temperature stability=Temperature stability of        piezoelectric response

Material properties of piezoelectric materials that are relevant totheir performance when used in acoustic wave filters include thefollowing:k _(t) ² =e ₃₃ ²/(c ^(D) ₃₃ε₃₃ ⁵)=d ₃₃ ²/(c ^(E) ₃₃ε₃₃ ^(T))=π²/4(1−(f_(s) /f _(p)))=K ²/(1+K ²): K=e ₃₃ ²ε_(R)ε₀ c ^(E) ₃₃

(k_(t) ² is the coupling coefficient, e₃₃ and d₃₃ are piezoelectriccoefficients, c^(D) ₃₃ and c^(E) ₃₃ are elastic moduli, ε₃₃ is thedielectric constant, and ε_(R) is the relative dielectric constant.f_(s) and f_(p) are the series and parallel resonance frequenciesrespectively.)

-   -   Signal to noise ratio (SNR)=e₃₁ ²/(ε₀ε₃₃ tan δ)^(1/2)    -   f_(s, m) (GHz)=Frequency of the point of minimum impedance,        which is close to and theoretically equal to the series        resonance frequency    -   f_(p) (GHz)=Parallel resonance frequency    -   Longitudinal sound velocity v₁=(c₃₃/ρ)^(1/2)    -   FOM (Figure of Merit)=k² _(eff, m)×Q

A chart of impedance vs. frequency for an example of an acoustic wavefilter showing locations of the series resonance frequency and theparallel resonance frequency is illustrated in FIG. 1.

At microwave frequencies, the dielectric constant of a material isdominated by ionic polarizability. A chart illustrating the dielectricpolarizabilities of various trivalent cations vs. crystal radius isillustrated in FIG. 2. The Clausius-Mossetti relation for dielectricconstant is as follows:−α_(D)=¾π[(V _(m))(ε′−1)/(ε′+2)]

-   -   α_(D)=total ionic polarizability    -   V_(m)=molar volume    -   ε′=dielectric constant of material        −α_(D)=Σα_(i)    -   α_(i) indicates individual ionic polarizabilities.        −ε′=(3V _(m)+8πα_(D))/(3V _(m)−4πα_(D))

Covalancy effects “blur” the ionic model. Doped AlN may showcharacteristics of both ionic and covalent bonding depending on thedopant(s) used.

AlN-based resonators show a temperature coefficient of frequency (TCF)drift in the range of −25 to −30 ppm/° C. For comparison, the TCF of GaNis about −18 ppm/° C. The TCF drift of the resonant frequency isdominated by the thermal drift in elastic modulus. Excess thermal driftof the resonant frequency is problematic in that a layer of silicondioxide (SiO₂) may need to be deposited on the resonator to compensatefor the TCF drift of the resonant frequency, leading to a reducedcoupling factor (k²) and spurious resonances. Doping AlN with a materialsuch as scandium (Sc) does little to adjust the TCF.

The sound velocity of a material is related to the bulk modulus anddensity of material per the equation:v=(K/ρ)^(1/2)

-   -   K=Bulk Modulus of Material    -   ρ=Density

The Longitudinal Sound Velocity of a material may be calculated by theformula:v ₁=(c ₃₃/ρ)^(1/2)

The acoustic velocities and other selected material parameters ofvarious electromechanical materials are illustrated in the table of FIG.3. 4H type hexagonal stacked silicon carbide (SiC) (Wurtzite) has a veryhigh sound velocity (13,100 m/s). A solid solution of AlN with SiC,however, is not feasible.

Various nitrides, including AlN, gallium nitride (GaN), and indiumnitride (InN) all assume the Wurtzite crystallographic structure withthe space group c⁴ _(6v). Space group refers to the 3 dimensionalsymmetry features shown in a periodic lattice. An illustration of thisstructure is shown in FIG. 4. The Wurtzite structure includestetrahedrally co-ordinated cations and anions in an AB type hexagonalstructure. The Wurtzite structure exhibits the highest symmetry possiblethat is compatible with spontaneous polarization. The keycrystallographic parameters of the Wurtzite crystal structure includehexagonal c, hexagonal a, and bond length u. These parameters areillustrated in FIG. 4. In AlN, the c-axis bond is elongated relative tothe others. These crystallographic parameters for AlN, GaN, and InN areas shown in Table 1 below:

TABLE 1 a (Å) c/a u (dimensionless) AlN 5.814 1.6190 0.380 GaN 6.0401.6336 0.376 InN 6.660 1.6270 0.377In the above table, u is the bond length. It is typically dimensionlessand expressed as a fraction of the dimensional c parameter. The bondlength in Å can be determined by (c/a) multiplied by u.

Wurtzite structured nitrides are more like II-VI materials (ZnO) ratherthan other III-V materials. Wurtzite structured nitrides have the samesign of piezoelectric coefficient and high Born effective charges(iconicity). Bond length (u) gets longer and c/a gets smaller fromGaN→InN→AlN. Various material parameters, including spontaneouspolarization, Born effective charge, and piezoelectric constants forvarious Wurtzite nitrides AlN, GaN, and InN and II-VI Wurtzite oxidesare illustrated in the table of FIG. 5A. Additional properties of AlN,GaN, and InN are illustrated in the table of FIG. 5B.

ZnO may be considered a model for Wurtzite structured III-V nitridessuch as AlN or GaN. ZnO has greater piezoelectric coefficients than AlNor GaN, a higher effective charge than GaN, and a greater polarizationresponse to strain than GaN. Enhanced piezoelectric response for smallercations substituting for Zn²⁺ in ZnO has been observed. Without beingbound to a particular theory, it is believed that the piezoelectricresponse in ZnO occurs due to the rotation of non-colinear bonds aroundthe c axis. The substitution of smaller highly charged ions for Zn ZnOenhances this rotation (e.g., substituting V⁵⁺ for Zn²⁺). Not many ionsare smaller than Al (for example, Si⁴⁺) in AlN, although this mechanismmay enhance piezoelectricity in GaN. The high charge on V⁵⁺ or Ta⁵⁺,possibly charge compensated with aluminum vacancies, may enhance thisrotation effect in AlN. Without being bound to a particular theory, itis also believed that defects may play a role in enhancement ofpiezoelectricity in doped ZnO and AlN since charge balance and theGrimm-Summerfeld concept are violated by the presence of defects. Chargecompensation may be accomplished by anti-site defects (N_(Al)), nitrogeninterstitials (N_(i)) or Al vacancies in doped AlN.

AlN exhibits various properties that have made it attractive for use asa piezoelectric material in acoustic wave resonators and filters. Theseproperties include:

-   -   Wide Bandgap (6.2 eV)    -   High Thermal Conductivity (2 W/cm-K)    -   High Electrical Resistivity (1×10¹⁶ Ω-cm)    -   High Breakdown Voltage (5×10⁵ V/cm)    -   High Quality Factor (3,000 at 2 GHz for BAW)    -   Moderate Coupling Coefficient (6.5% for BAW)    -   Moderate Piezoelectric Coefficient (e₃₃=1.55 C/m2)    -   High Longitudinal Acoustic Velocity (11,300 m/s for BAW)    -   Low Propagation Losses    -   Easy to prepare c-axis oriented films    -   Chemically stable    -   Compatible with IC-technology processes

Other than BN, very little work has been performed to characterize thepiezoelectric properties of IIIA nitride—AlN solid solutions. Theresults of examination of the lattice constant and energy gap ofAl_(x)Ga_(1-x)N solid solutions are illustrated in FIGS. 6A and 6B.Al_(x)Ga_(1-x)N exhibits a continuous solid solution.

Additional work comparing the properties of SiC, GaN, InN, ZnO, and CdSehas shown that decreasing Phillips Tonicity leads to larger elasticconstants and larger sound velocities as illustrated in FIGS. 7A and 7B.

The properties of AlN doped with Sc have been investigated. ScN has arock salt structure. The c/a ratio in the Wurtzite structure of AlNdecreases with Sc additions (c/a for AlN is 1.601; c/a forAl_(0.88)Sc_(0.12)N is 1.575). Modelling predicts that intermediatehexagonal crystallographic structures may be present in Sc-doped AlN.The change in crystallographic structure vs. c/a ratio forSc_(0.5)Al_(0.5)N is illustrated in FIGS. 8A and 8B. FIGS. 8A and 8Bultimately indicate the same c/a ratio and show the energy penalty paidin deviating from the optimum c/a ratio. The u parameter is largeraround. Sc sites. There is a shallow energy well in the c direction. Scdecreases co-valency and increases piezoelectricity of the doped AlN.Density functional theory reveals that the substitution of Sc for Alleads to the softening of the Wurtzite phase. This is due to acompetition of Al³⁺ and Sc³⁺ about the coordination of nitrogen. Al³⁺prefers tetrahedral coordination whereas Sc³⁺ prefers 5 or 6 foldcoordination. This leads to a frustrated system. Potential wells forions become less deep and ionic displacements become larger as Sc issubstituted for Al in AlN. With increased concentrations of Sc the e₃₃piezoelectric coefficient increases while the c₃₃ elastic constantdecreases. Larger, more electropositive ions like Y³⁺, Yb³⁺, etc. mayalso exhibit this effect. A comparison between various properties of AlNand Al_(0.88)Sc_(0.12)N is illustrated in FIG. 8C and comparisonsbetween the properties of AlN and AlN doped with other concentrations ofSc are illustrated in FIGS. 8D-8H.

Another doped AlN material that has been studied to some extent isY_(x)Al_(1-x)N. Yttrium has a larger ionic radius, is moreelectropositive, and is less costly than scandium. Ab initiocalculations based on density functional theory indicate high phasestability for the Wurtzite structure of Y_(x)Al_(1-x)N (x=0.75).Nonetheless poor crystallinity has been observed in Y_(x)Al_(1-x)Nfilms. Y_(x)Al_(1-x)N exhibits a large affinity for oxygen and water(YOOH groups). The band gap of Y_(x)Al_(1-x)N is reduced from 6.2 eV(AlN) to 4.5 eV at x=0.22. A larger decrease in elastic coefficient anda larger increase in d₃₃ and e₃₃ is observed in Y_(x)Al_(1-x) than inSc-doped AlN. The observed increase in permittivity for Y_(x)Al_(1-x)Nis similar to Sc-doped material. Charts illustrating the change inε_(r), e₃₃, e₃₁, d₃₃, and d₃₁ with different amounts of Y dopant inY_(x)Al_(1-x)N are illustrated in FIGS. 9A-9C.

There has been some work performed investigating the properties of AlNwith coupled substitution of Mg and Zr, Mg and Ti, or Mg and Hf for Al.These materials exhibit improved piezoelectric coefficients relative toAlN but lower elastic coefficients (and likely sound velocities and Q).Charts illustrating the piezoelectric coefficients and elasticcoefficients of AlN with coupled substitution of Mg and Zr, Mg and Ti,and Mg and Hf for Al for different dopant concentration are illustratedrelative to piezoelectric coefficients and elastic coefficients ofSc_(x)Al_(1-x)N in FIGS. 10A and 10B. Various properties of(Mg_(0.5)Zr_(0.5))_(0.13)Al_(0.87)N and(Mg_(0.5)Hf_(0.5))_(0.13)Al_(0.87)N vs. those of AlN are tabulated inFIG. 10C.

Numerous studies have been performed on Wurtzite B_(x)Al_(1-x)N_(y)(0.001<x<0.70, 0.85<y<1.05). Films having up to 8% B have beensuccessfully synthesized. Ab initio results indicate that increasedcovalency indicates increases in the elastic constant c₃₃ and theacoustic velocity with increasing B. Decreased ionicity leads todecreased e₃₃ and k² with increasing boron concentration. Dielectricconstant is expected to decrease with increasing boron concentration.Boron addition to AlN leads to greater hardness, higher sound velocity,and a wider band gap than un-doped AlN films. Peak broadening isobserved due to structural disorder and increased c/a ratio. The latticeconstants of synthesized films decrease more than predicted by Vegard'slaw. Calculated and observed material properties for B_(x)Al_(1-x)N_(y)with different quantities of B are illustrated in the graphs of FIGS.11A-11F.

AlN with Cr or Mn substituted for Al in AlN has been investigated foruse as dilute magnetic semiconductors. Sputtered films showed goodc-axis orientation. The resistivity of Al_(0.93)Cr_(0.07)N andAl_(0.91)Mn_(0.09)N vs. temperature is illustrated in FIG. 12A.Additional material properties of Cr-doped AlN are illustrated in FIGS.12B and 12C. The Mn-doped material shows a higher resistivity thanCr-doped material. Specifically with regard to the Cr-doped material, no3d transition metal shows as marked a preference for octahedralcoordination as Cr³⁺. Therefore, forcing Cr into AlN would likely causedistortions potentially enhancing k². CrN is isostructural with ScN(halite structure). XPS binding energy indicates that Cr is present inCr-doped AlN as Cr³⁺. XANES peak for disallowed 1s-3d transitionindicates Cr is present in low symmetry (tetrahedral) sites. Cr induceslattice strain and deforms the AlN Wurtzite structure. The soundvelocity of Al_(0.937)Cr_(0.063)N (11,490 m/s) is greater than that ofun-doped AlN. Al_(0.937)Cr_(0.063)N has been observed to exhibit a lowerk² (5.6%) than AlN (7.9%), higher TCF values (−39 ppm/° C.), and higherε′ (Capacitance) 91 pF/m vs. 82 pF/m for substituted AlN, which isunexpected in that most other substitutions which decrease the couplingfactor also decrease the dielectric constant (and thus the capacitance).Inversion domains (Regions of opposite polarity) have been observed.Ferromagnetism has been observed in Cr³⁺ doped AlN.

Ti may also be substituted for Al in AlN. In such materials, theoxidation state of the Ti is unknown, although presumed to be Ti³⁺.Al—Ti—N films form a single phase Wurtzite structure when Ti content isless than 16%. Large Ti atoms cause a shift in the 2 theta values forx-ray diffraction peaks. Crystal lattice parameters increase withincreasing concentrations of Ti. Compressive strains reducecrystallinity when additional Ti is added. Ti—Al segregation has beenobserved above 4% Ti. Sound velocity and k² decrease with increasing Ticontent. Dielectric constant increases with Ti content. The TCF ofTi-doped AlN is slightly lower than that of AlN. FIG. 13 illustrates theelectromechanical coupling factor, longitudinal velocity, and dielectricconstant of Al_((0.5-x))Ti_(x)N_(0.5) as a function of x.

Additional elements that may be substituted for Al in AlN includetantalum (Ta) and vanadium (V). The oxidation states of these elementswhen substituting for Al in AlN are assumed to be Ta³⁺ and V³⁺. Thecrystallographic c parameter is reduced when AlN is doped with V, butincreased when AlN is doped with Ta. When AlN is doped with more thanabout 7% V, the crystallinity of the material is destroyed. A VN phasebegins to appear at 6.4% V. For Ta, segregation is observed when Ta isdoped into AlN at 3.2% or more. Acoustic velocity and k² drop as Vcontent increases, but ε′ increases. Charts illustrating changes inacoustic velocity and dielectric constant of AlN doped with varyingamounts of V and Ta are illustrated in FIGS. 14A and 14B, respectively.

The limit for Al substitution by Ta in AlN appears to be 5.1 atomicpercent. Ta may be substituted for Al in AlN with excellent c-axisorientation. Like Sc³⁺, Ta⁵⁺ is larger than Al³⁺. However, unlike withSc³⁺ substitution, the c/a ratio does not decrease with substitution ofAl³⁺ in AlN with Ta⁵⁺. Instead, both c and a lattice constants increase.FIG. 14C illustrates how the c and a lattice constants in AlN changewith different amounts of Ta doping. Raman, TEM and XPS suggest nosecond phases or compositionally inhomogeneous regions appear with Tasubstitution for Al in AlN. Elastic losses within the Ta—Al—N crystallattice may be due to disorder due to defects. Ta⁵⁺ is lesselectropositive than Sc³⁺, however a large increase in d₃₃ is observedin Ta-doped AlN. (See FIG. 14D.) It has been hypothesized that theincrease in d₃₃ observed in Ta-doped AlN may be due to ease of bondbending. Small ions promote bond rotation. Small ions may be easilymoved under an applied electric field (e.g., V⁵⁺ in ZnO). A similareffect may apply to Ta⁵⁺ in AlN because of large lattice expansion. Ta⁵⁺is not expected to be that much smaller than Al³⁺ so it is uncertain whythere is an increase in the d₃₃ piezoelectric coefficient. This ispossibly associated with charge compensating defects.

In some examples, AlN may be doped with oxygen. For example, oxygen maybe present in sputtering gas used during deposition of MN-based films.Despite the increasing ionicity of oxygen, the magnitude of thepiezoelectric coefficient of oxygen-doped AlN does not increase. Withoutbeing bound to a particular theory, it is possible that oxygen defectsin AlN may be compensated by aluminum vacancies (□_(Al)). Further, thepresence of oxygen in AlN may cause second phase Al₂O₃ to form. It thusmay be difficult to control the anion stoichiometry. Accordingly, indoped AlN, it may be preferable to avoid anion mixing, but rather tomake all adjustments on a cation basis.

The addition of dopants into AlN may cause one or more of a number oftypes of crystallographic defects. One type of defect involveselectronic substitutions. For example, Si substituted for Al in AlN mayact as a deep level donor (320 meV) which may reduce the conductivity ofthe material, while C substituted for Al in AlN may act as a deep levelacceptor (500 meV). Point defects include vacancies, interstitials, andanti-site defects. In AlN, vacancies are more energetically favorablethan interstitials or anti-site defects. For Al vacancies atomicdisplacement away from the vacancy is observed. For N vacancies atomicdisplacement toward the vacancy is observed. Stacking faults in AlNinclude {1120} stacking fault configurations. Stacking faults may be apreferred region for substitutional ions or M vacancies. Systematicvacancies may be caused by substitution of Al in AlN by some elements.For example, Ta⁵⁺ and Zr⁴⁺ doping of AlN would be compensated for bynative defects such as Al vacancies (V_(Al) or □_(Al)). Smaller ionsthan Al³⁺ or Ta⁵⁺ may form elastically driven defect couples with2□_(Al)−3Ta_(Al). The □_(Al) and Ta_(Al) vacancies or substitutions mayexpand nearest neighbor N tetrahedral. Si⁴⁺ may contract nearestneighbor N tetrahedral forming defect couples with V_(Al).

SUMMARY

In accordance with a first aspect, there is provided a piezoelectricmaterial. The piezoelectric material comprises AlN doped with cations ofone or more elements selected from the group consisting of: one of Sb,Ta, Nb, or Ge; Cr in combination with one or more of B, Sc, Y, Sm, Eu,Gd, Tb, Dy, Ho, Er, Tm, or Yb; one of Nb and Ta in combination with oneof Li, Mg, Ca, Ni, Co, and Zn; Ca in combination with one of Si, Ge, Ti,Zr, and Hf; Mg in combination with one of Si, Ge, and Ti; and one ormore of Co, Sb, Ta, Nb, Si, or Ge in combination with one or more of Sm,Eu, Gd, Tb, Dy, Ho, Er, Tm, or Yb. The cations at least partiallysubstitute for Al in the crystal structure of the piezoelectricmaterial.

In some embodiments, the piezoelectric material has one of the formulasAl_(1-x)Ge_(3/4x)□_(1/4x)N or Al_(1-5/3x)Ta⁵⁺ _(x)□_(2/3x)N, □representing a vacancy in an Al site in the crystal structure of thepiezoelectric material, 0<x<0.25.

In some embodiments, the piezoelectric material has the formulaAl_(1-2x)B_(x)Cr_(x)N 0<x<0.15.

In some embodiments, the piezoelectric material has the formulaAl_(1-5/3x-3y)Mg_(2y)Ta_(x+y)□_(2/3x)N, □ representing a vacancy in anAl site in the crystal structure of the piezoelectric material,1>5/3x+3y, 0<x<0.3, 0<y<0.25.

In some embodiments, the piezoelectric material has the formulaAl_(1-2x)Mg_(x)Si_(x)N 0<x<0.15.

In some embodiments, the piezoelectric material has the formulaAl_(1-x-y)Cr³⁺ _(x)M^(III) _(y)N, M^(III)=Sc³⁺, Y³⁺, Sm³⁺ . . . Yb³⁺,Sm³⁺ . . . Yb³⁺=any one or more of the Lanthanides with atomic numbersfrom 62-70.

The piezoelectric material may have a Wurtzite crystal structure.

In some embodiments, an acoustic wave resonator includes thepiezoelectric material. The acoustic wave resonator may be configured asa solidly mounted resonator. The acoustic wave resonator may beconfigured as a film bulk acoustic resonator.

In some embodiments, a filter includes the acoustic wave resonator. Thefilter may have a passband in the radio frequency hand.

In some embodiments, an electronic device module includes the filter.

In some embodiments, an electronic device includes the electronic devicemodule. The electronic device module may be a radio frequency electronicdevice module.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a chart of impedance vs. frequency for an example of anacoustic wave filter;

FIG. 2 is a chart illustrating the dielectric polarizabilities ofvarious trivalent cations vs. crystal radius;

FIG. 3 is a table of selected material parameters of variouselectromechanical materials;

FIG. 4 illustrates t Wurtzite crystallographic structure;

FIG. 5A is a table of selected material parameters for various III-VWurtzite nitrides and II-VI Wurtzite oxides;

FIG. 5B is a table of selected material parameters of AlN, GaN, and InN;

FIG. 6A is a chart of lattice constant vs. x in Al_(x)Ga_(1-x)N;

FIG. 6B is a chart of energy gap vs. x in Al_(x)Ga_(1-x)N;

FIG. 7A is a chart of elastic constant vs. Phillips Ionicity forselected compounds;

FIG. 7B is a chart of sound velocity vs. Phillips Ionicity for selectedcompounds;

FIG. 8A is a chart illustrating the change in crystallographic structurevs. c/a ratio in Sc_(0.5)Al_(0.5)N;

FIG. 8B is another chart illustrating the change in crystallographicstructure vs c/a ratio in Sc_(0.5)Al_(0.5)N;

FIG. 8C is a table of select material properties of AlN andAl_(0.88)Sc_(0.12)N.

FIG. 8D is a table of select material properties of AlN and AlN dopedwith various concentrations of Sc.

FIG. 8E is a chart of k² and Q-factor for AlN doped with variousconcentrations of Sc;

FIG. 8F is a chart of ε_(r) and tan δ for AlN doped with variousconcentrations of Sc;

FIG. 8G is a chart of FOM for AlN doped with various concentrations ofSc;

FIG. 8H is a chart of TCF for AlN doped with various concentrations ofSc;

FIG. 9A is a chart of ε_(r) for AlN doped with various concentrations ofY;

FIG. 9B is a chart of e₃₃ and e₃₁ for AlN doped with variousconcentrations of Y;

FIG. 9C is a chart of d₃₃, and d₃₁ for AlN doped with variousconcentrations of Y;

FIG. 10A is a chart of e₃₃ vs. dopant concentration for AlN doped withSc, and with coupled substitution of Mg and Zr, Mg and Ti, and Mg and Hffor Al;

FIG. 10B is a chart of c₃₃ vs. dopant concentration for AlN doped withSc, and with coupled substitution of Mg and Zr, Mg and Ti, and Mg and Hffor Al;

FIG. 10C is a table of selected material properties of AlN,(Mg_(0.5)Zr_(0.5))_(0.13)Al_(0.87)N and(Mg_(0.5)Hf_(0.5))_(0.13)Al_(0.87)N;

FIG. 11A is a chart of c₃₃ vs. boron concentration in boron-doped AlN;

FIG. 11B is a chart of e₃₃ vs. boron concentration in boron-doped AlN;

FIG. 11C is a chart of crystal lattice parameter c vs. boronconcentration in boron-doped AlN;

FIG. 11D is a chart of k² vs. boron concentration in boron-doped AlN;

FIG. 11E is a chart of crystal unit cell volume vs. boron concentrationin boron-doped AlN;

FIG. 11F is a chart of crystal lattice parameters c and a vs. boronconcentration in boron-doped AlN;

FIG. 12A is a chart of material resistivity vs. temperature forAl_(0.93)Cr_(0.07)N and Al_(0.91)Mn_(0.09)N;

FIG. 12B is a chart of lattice constant vs. Cr concentration in Cr-dopedAlN;

FIG. 12C is a chart of effective d₃₃ vs. Cr concentration in Cr-dopedAlN;

FIG. 13 is a chart of k², v_(s), and dielectric constant vs. Ticoncentration in Ti-doped AlN;

FIG. 14A is a chart of acoustic velocity and dielectric constant vs. Vcontent V-doped AlN;

FIG. 14B is a chart of acoustic velocity and dielectric constant vs. Tacontent in Ta-doped AlN;

FIG. 14C is a chart of lattice constant vs. Ta content in Ta-doped AlN;

FIG. 14D is a chart of piezoelectric coefficient d₃₃ vs. Ta content inTa-doped AlN;

FIG. 15 illustrates conflicting tradeoffs in materials properties fordifferent dopants in AlN;

FIG. 16 is a table indicating the expected effect of various dopants onselected material properties of doped AlN;

FIG. 17 is a cross-sectional view of an example of a solidly mountedresonator (SMR) BAW;

FIG. 18 is a cross-sectional view of an example of an FBAR BAW; and

FIG. 19 is a schematic view of a filter than may include SMR BAW and/orFBAR BAW devices;

FIG. 20 is a block diagram of a front-end module in which the filter ofFIG. 19 may be implemented; and

FIG. 21 is a block diagram of a wireless device in which the filter ofFIG. 19 may be implemented.

DETAILED DESCRIPTION

Analysis of crystal chemical systematic from previous work has providedinsights into how specific chemical substituents for aluminum (Al) inaluminum nitride (AlN) affect various properties of interest of thematerial. Disclosed herein are new chemical substituent combinations forAlN that may be used to form a piezoelectric material for use inacoustic wave filters such as Bulk Acoustic Wave (BAW) and Film BulkAcoustic Resonator (FBAR) filters. Advantages of the solutions disclosedherein over previous solutions are that multiple material properties maybe simultaneously optimized (for example, electromechanical coupling andsound velocity). Based on the knowledge of crystal chemistry andprevious work, there appears to be a series of mutually exclusiveproperty combinations resulting from doping for Al in AlN-basedpiezoelectric materials. For example, substitutions which form a moreionic bond with nitrogen than aluminum (such as scandium) will improvethe coupling and dielectric constant whereas substitutions which form amore covalent bond with nitrogen than aluminum (such as boron) willimprove the sound velocity and decrease viscoelastic losses. Disclosedherein are AlN-based piezoelectric materials which may exhibitimprovements in multiple properties or which may exhibit extremeenhancements for specific individual properties (e.g. dielectricconstant).

The most frequently cited additive to AlN is scandium (Sc). Scandium ismore electropositive than Al. Increased Tonicity of Sc³⁺ relative toAl³⁺ increases the piezoelectric coupling of Sc-doped AlN as compared toun-doped AlN. Sc³⁺ is also larger than Al³⁺. Distortion of the crystallattice of AlN due to the presence of Sc³⁺ substituted for Al³⁺increases the piezoelectric coefficient of Sc-doped AlN as compared toun-doped AlN. The loss of covalency due to the presence of Sc³⁺substituted for Al³⁺ however, increases viscoelastic losses.

Y, Yb and other small lanthanides are larger ions than Sc³⁺ and are moreelectropositive than Sc. Substitution of Al³⁺ in AlN with ions of theseelements may enhance both piezoelectric effect and viscoelastic losses.Heavier polarizable atoms such as Yb³⁺ should improve the dielectricconstant of the doped AlN more than lighter atoms such as Sc³⁺ and Y³⁺.Multiple isovalent substitutions (AlN:B, Sc or AlN:B, Yb) may also beused.

In contrast with Sc, Y, and Yb, boron (B) forms a much smaller ion thanAl and is less electropositive than Al. Boron would form a more covalentbond with N than Al. Piezoelectric coupling may be expected to decreaseslightly with B substitution for Al in AlN, but viscoelastic lossesshould decrease as well. The increased covalency of B—N bonds relativeto Al—N bonds should increase the bulk modulus of B-doped AlN ascompared to un-doped AlN. Light B atoms substituting for Al should alsodecrease the density of B-doped AlN as compared to un-doped AlN. Botheffects should combine to give greater acoustic velocity (v=(K/ρ)^(1/2),K=Bulk Modulus of Material; ρ=Density).

Dopants for Al in AlN which enhance Q, elastic modulus, and soundvelocity of the material appear to work against improved couplingcoefficients and higher dielectric constants. This is representedschematically in FIG. 15. Simultaneous additions of different dopantsand/or doping AlN to facilitate 3d electron interactions or to formordered vacant lattice sites may provide the benefits associated withboth highly electropositive and weakly electropositive dopants.

In transition metals, the d-electron manifold greatly complicatesbonding. Ions may have preference for octahedral or tetrahedralcoordination depending on d electron count. For example, Cr³⁺ hasextremely strong preference for octahedral coordination. If forced intoa tetrahedral site, this may create strong lattice distortions enhancingpiezoelectricity (even though the Cr³⁺ ion is not as electropositive asSc). Coupled substitution of B and Cr may produce lattice distortionsenhancing piezoelectricity without viscoelastic losses. Other ions suchas V³⁺, Mn³⁺, and Co³⁺ can be useful as dopants to improve theproperties of AlN. These ions can adjust to different oxidation stateswith Co³⁺ having several spin states per oxidation state and can thusexhibit multiple different ionic radii.

In some embodiments, vacant lattice sites (0 electrons) may also beincorporated into the tetrahedral framework of Grimm-Summerfeld rules.An example is γ-Ga₂S₃ which is a 3₂06₃ type. Aluminum vacancies in AlNmay be considered a quadruplet of non-bonding orbitals (lone pairs) inthe tetrahedral structure. Aluminum vacancies in AlN may increaseviscoelastic losses (especially if mobile) or enhance piezoelectricdistortion without increasing ionicity.

Other compounds which may be useful in mixing with AlN to form a dopedAlN material include the 4₃05₄ compounds such as Si₃N₄ and Ge₃N₄. Ge₃N₄crystallizes in a defect-containing Wurtzite structure where cationvacancies are ordered. Increasing p orbital character in non-bondingorbitals leads to the tendency for sp² (planar) hybridization of bondingorbitals which may distort lattice the crystal lattice. Solid solutionssuch as Al_(1-x)Ge_(3/4x)□_(1/4x)N and Al_(1-x)Si_(3/4x)□_(1/4x)N arealso of interest, where □ represents a vacancy in an Al site of thecrystal structure of the piezoelectric material.

In solid solutions of AlN with GaN and InN, k² and sound velocity areexpected to drop. The dielectric constant of the material may thereforeincrease slightly relative to un-doped AlN along with the c/a ratio dueto assumed linear relationships in properties.

The expected effect of various dopants on various material properties ofAlN are tabulated in FIG. 16.

A listing of different AlN based piezoelectric materials that mayexhibit desirable properties for use in acoustic wave resonators orfilters and the expected effect of the dopant(s) on the base AlNmaterial is presented in Table 2 below:

TABLE 2 Compound Formula Expected Effect of Dopant(s) Al_(1−x)(Sm³⁺ . .. Yb³⁺)_(x)N Yb³⁺ is larger more electropositive ion than Sm³⁺ . . .Yb³⁺ = any one or more of the Sc³⁺ and smaller and more electropositivethan Lanthanides with atomic numbers from Y³⁺. 62-70. Sm³⁺ is larger andmore electropositive than both Sc³⁺ and Y³⁺ and has a high Shannonpolarizability to improve dielectric constant. As dopant levelincreases, expect to decrease Q and increase k² and dielectric constant.The sound velocity should decrease as well. Higher ionicities than Sc—Nbond. Expect higher dielectric constants than Sc doped AlN.Al_(1−x−y)B_(x)M^(III) _(y)N Boron and M^(III) will work in oppositedirections. M^(III) = Sc³⁺, Y³⁺, Sm³⁺ . . . Yb³⁺ Three different sizedions on Al site may This is a combination of boron and Sc³⁺ negativelyimpact Q. or one or more electropositive ions such as Y³⁺ or Yb³⁺. Thenumber of cation substitutions may be limited to three or less.Al_(1−x−y)B_(x)Cr³⁺ _(y)N Potential for high sound velocity materialwith This is a combination of boron and Cr³⁺. modest decreases in thecoupling as compared to B substitution alone. Both B and Cr are reportedto increase the sound velocity. They oppose each other with regard to k²and ε′. Al_(1−x−y)Cr³⁺ _(x)M^(III) _(y)N Potential for a high k² and ε′material without M^(III) = Sc³⁺, Y³⁺, Sm³⁺ . . . Yb³⁺ significantreduction in sound velocity or This is a combination of Cr and Sc³⁺ orviscoelastic losses. Improved Q a possibility. Cr one or moreelectropositive ions such as induces lattice strain and deforms WurziteY³⁺ or Yb³⁺. structure. Al_(1−x)Co_(x)N Co readily adapts 2+, 3+ and 4+oxidation states and each oxidation state has multiple spin statesleading to a set of potential ionic sizes. Single doping will likelylead to 3+ state but 4+ and 2+ states may be induced by co-doping withMg²⁺ or Zr⁴⁺ (or Hf⁴⁺) respectively. Reduced electrical conductivity isa risk at high doping levels. Al_(1−x)Sb³⁺ _(x)N Sb³⁺ shows very highionic polarizabilities leading to the potential for enhanced dielectricconstant either for single doping or coupled doping with other ions.However, there is a risk that the Sb will adopt the Sb⁻³ state andsubstitute for Nitrogen. The effect on k² is uncertain since the lonepair would enhance asymmetry in the Al site but the increased covalencywould not. Al_(1−5/3x)Ta⁵⁺ _(x□2/3x)N Improvement in the piezoelectriccoefficient □ = Aluminum vacancy expected for small additions of Ta.Al_(1−3x)Mg_(2x)Ta⁵ _(x)N Improvement in the piezoelectric coefficientis observed for small additions. Expect similar improvement in k² as theMg/Zr or Mg/Hf co-doped materials with higher ε′ due to higherpolarizability than Zr or Hf. Acoustic velocity effect unknown.Al_(1−5/3x−3y)Mg²⁺ _(2y)Ta⁵⁺ _(x+y□2/3x)N There can be a continuousseries of Ta additives compensated by vacancies and Mg²⁺. Expect similarimprovement in k² as the Mg/Zr or Mg/Hf co-doped materials with higherε′ due to higher polarizability than Zr or Hf. Acoustic velocity effectunknown. Al_(1−5/3x−3y)Li⁺ _(y)Ta⁵⁺ _(x+y□2/3x)N Expect similarimprovement in k2 as the Mg/Zr or Mg/Hf co-doped materials with higherε′ due to higher polarizability than Zr or Hf. Acoustic velocity effectunknown. Al_(1−5/3x)Nb⁵⁺ _(x□2/3x)N, Al_(1−3x)Mg²⁺ _(x)Nb⁵⁺ _(x)N, Samechemistries as with Ta⁵⁺. Al_(1−5/3x−3y)Li⁺ _(y)Nb⁵⁺ _(x+y□2/3x)N, orNb⁵⁺ more likely to be reduced than Ta⁵⁺. Al_(1−5/3x−3y)Mg²⁺ _(2y)Nb⁵⁺_(x+y□2/3x)N Combinations of Nb and Ta as well. Al_(1−x)Ge_(3/4x□1/4x)Nor Al_(1−x)Si_(3/4x□1/4x)N Possible increase in piezoelectriccoefficient and Si and Ge doping. coupling without significant decreasein sound velocity. However, it is likely Si and Ge partition onto boththe AlN sites without the need charge compensating defects. Covalencywould increase in both cases. Al_(1−2x)Mg²⁺ _(x)Si⁴⁺ _(x)N Using Mg²⁺ tobias Si into Al site for charge compensation. Possible double effect onk² and d₃₃. Large electropositive ions will boost k². The Si⁴⁺ maybehave as a small charged ion (as in doped ZnO) and contribute to thek². More likely, it will enhance covalence and potentially give asolution with enhanced k² without the sound velocity degradation andviscoelastic losses. Al_(1−2x)Mg²⁺ _(x)Ti⁴⁺ _(x)N Ti³⁺ may forms andMg_(Al) may be charge compensated with Magnesium vacancies. d⁰ states in1st row transition metals such as Ti⁴⁺ and V⁵⁺ unlikely to be stabilizedin AlN.

As discussed above, the various materials disclosed herein may be usefulas piezoelectric materials in BAW resonators. In some implementations,the various materials disclosed herein may also be useful aspiezoelectric materials in surface acoustic wave (SAW) resonators orfilters. One type of BAW resonator is a solidly mounted resonator (SMR).One example of an SMR BAW is illustrated in FIG. 17, generally at 100.The SMR BAW is formed on a substrate 105, for example, a siliconsubstrate. A layer of piezoelectric material 110 is disposed on thesubstrate 105 between an upper electrode 115 and a lower electrode 120.The layer of piezoelectric material 110 may include or consist of any ofthe materials disclosed herein. The layer of piezoelectric material 110has a thickness of λ/2, where λ is the resonant frequency of the SMR BAW100. A Bragg reflector or acoustic mirror 125 including alternatinglayers of high impedance material 130, for example, SiO₂, and lowimpedance material 135, for example, Mo or W, is disposed below thelower electrode 120 and helps confine acoustic energy to thepiezoelectric material 110 rather than leaking away through thesubstrate 105. Each layer of material 120, 135 may have a thickness ofλ/4.

An example of an FBAR BAW is illustrated in FIG. 18, generally at 200.The FBAR BAW 200 includes a piezoelectric material film 210 disposed ona substrate 205, for example, a silicon substrate, between an upperelectrode 215 and a lower electrode 220. A cavity 225 is formed belowthe piezoelectric material film 210 (and optionally below the lowerelectrode 220) and above the upper surface of the substrate 205 to allowfor the piezoelectric material film 210 to vibrate. The piezoelectricmaterial film 210 may include or consist of any of the materialsdisclosed herein.

Examples of SMR BAW and/or FBAR BAW resonators including any of thematerials disclosed herein as their piezoelectric elements may becombined together to form a filter. One example of a filter arrangementthat may be useful in filtering signals in the radio frequency (RF)range may be a ladder filter 300 as illustrated schematically in FIG.19. The ladder filter 300 includes a plurality of series resonators R1,R2, R3, R4, R5, R6 connected in series between an input port 305 and anoutput port 310 and a plurality of parallel resonators R7, R8, and R9having first sides electrically connected between a pair of the seriesresonators and second sides electrically connected to a referencevoltage, for example, ground. The resonant and anti-resonant frequenciesof the resonators R1-R9 may be selected such that the ladder filter 300passes RF energy within a desired passband from the input port 305 tothe output port 310 while attenuating RF energy at frequencies outsideof the passband. It should be appreciated that the number andarrangement of series and/or parallel resonators included in the ladderfilter may vary based on the desired frequency response of the filter.

Referring to FIG. 20, there is illustrated a block diagram of oneexample of a front-end module 400, which may be used in an electronicdevice such as a wireless communications device (e.g., a mobile phone)for example. The front-end module 400 includes an antenna duplexer 410having a common node 412, an input node 414, and an output node 416. Anantenna 510 is connected to the common node 412. The front-end module400 further includes a transmitter circuit 432 connected to the inputnode 414 of the duplexer 410 and a receiver circuit 434 connected to theoutput node 416 of the duplexer 410. The transmitter circuit 432 cangenerate signals for transmission via the antenna 510, and the receivercircuit 434 can receive and process signals received via the antenna510. In some embodiments, the receiver and transmitter circuits areimplemented as separate components, as shown in FIG. 20; however inother embodiments these components may be integrated into a commontransceiver circuit or module. As will be appreciated by those skilledin the art, the front-end module 400 may include other components thatare not illustrated in FIG. 20 including, but not limited to, switches,electromagnetic couplers, amplifiers, processors, and the like.

The antenna duplexer 410 may include one or more transmission filters422 connected between the input node 414 and the common node 412, andone or more reception filters 424 connected between the common node 412and the output node 416. The passband(s) of the transmission filter(s)are different from the passband(s) of the reception filters. Each of thetransmission filter(s) 422 and the reception filter(s) 424 may includeone or more resonators including one or more embodiments of thepiezoelectric material as disclosed herein. An inductor or othermatching component 440 may be connected at the common node 412.

In certain examples, each of the acoustic wave elements used in thetransmission filter 422 or the reception filter 424 include the samepiezoelectric material. This structure reduces the effect of changes intemperature upon the frequency responses of the respective filter, inparticular, reducing degradation in the passing or attenuationcharacteristics due to changes in the temperature, because each acousticwave element changes similarly in response to changes in the ambienttemperature.

FIG. 21 is a block diagram of one example of a wireless device 500including the antenna duplexer 410 shown in FIG. 20. The wireless device500 can be a cellular phone, smart phone, tablet, modern, communicationnetwork or any other portable or non-portable device configured forvoice or data communication. The wireless device 500 can receive andtransmit signals from the antenna 510. The wireless device includes anembodiment of a front-end module 400′ similar to that discussed abovewith reference to FIG. 20. The front-end module 400′ includes theduplexer 410, as discussed above. In the example shown in FIG. 21 thefront-end module 400′ further includes an antenna switch 450, which canbe configured to switch between different frequency hands or modes, suchas transmit and receive modes, for example. In the example illustratedin FIG. 21, the antenna switch 450 is positioned between the duplexer410 and the antenna 510; however, in other examples the duplexer 410 canbe positioned between the antenna switch 450 and the antenna 510. Inother examples the antenna switch 450 and the duplexer 410 can beintegrated into a single component.

The front end module 400′ includes a transceiver 430 that is configuredto generate signals for transmission or to process received signals. Thetransceiver 430 can include the transmitter circuit 432, which can beconnected to the input node 414 of the duplexer 410, and the receivercircuit 434, which can be connected to the output node 416 of theduplexer 410, as shown in the example of FIG. 20.

Signals generated for transmission by the transmitter circuit 432 arereceived by a power amplifier (PA) module 460, which amplifies thegenerated signals from the transceiver 430. The power amplifier module460 can include one or more power amplifiers. The power amplifier module460 can be used to amplify a wide variety of RF or other frequency-bandtransmission signals. For example, the power amplifier module 460 canreceive an enable signal that can be used to pulse the output of thepower amplifier to aid in transmitting a wireless local area network(WLAN) signal or any other suitable pulsed signal. The power amplifiermodule 460 can be configured to amplify any of a variety of types ofsignal, including, for example, a Global System for Mobile (GSM) signal,a code division multiple access (CDMA) signal, a W-CDMA signal, a LongTerm Evolution (LTE) signal, or an EDGE signal. In certain embodiments,the power amplifier module 460 and associated components includingswitches and the like can be fabricated on gallium arsenide (GaAs)substrates using, for example, high-electron mobility transistors(pHEMT) or insulated-gate bipolar transistors (BiFET), or on a Siliconsubstrate using complementary metal-oxide semiconductor (CMOS) fieldeffect transistors.

Still referring to FIG. 21, the front-end module 400′ may furtherinclude a low noise amplifier module 470, which amplifies receivedsignals from the antenna 510 and provides the amplified signals to thereceiver circuit 434 of the transceiver 430.

The wireless device 500 of FIG. 21 further includes a power managementsub-system 520 that is connected to the transceiver 430 and manages thepower for the operation of the wireless device 500. The power managementsystem 520 can also control the operation of a baseband sub-system 530and various other components of the wireless device 500. The powermanagement system 520 can include, or can be connected to, a battery(not shown) that supplies power for the various components of thewireless device 500. The power management system 520 can further includeone or more processors or controllers that can control the transmissionof signals, for example. In one embodiment, the baseband sub-system 530is connected to a user interface 540 to facilitate various input andoutput of voice and/or data provided to and received from the user. Thebaseband sub-system 530 can also be connected to memory 550 that isconfigured to store data and/or instructions to facilitate the operationof the wireless device, and/or to provide storage of information for theuser.

Having described above several aspects of at least one embodiment, it isto be appreciated various alterations, modifications, and improvementswill readily occur to those skilled in the art. Such alterations,modifications, and improvements are intended to be part of thisdisclosure and are intended to be within the scope of the invention. Itis to be appreciated that embodiments of the methods and apparatusesdiscussed herein are not limited in application to the details ofconstruction and the arrangement of components set forth in theforegoing description or illustrated in the accompanying drawings. Themethods and apparatuses are capable of implementation in otherembodiments and of being practiced or of being carried out in variousways. Examples of specific implementations are provided herein forillustrative purposes only and are not intended to be limiting. One ormore features of any embodiment disclosed herein may be added to orsubstituted for any one or more features of any other embodiment. Also,the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use herein of“including,” “comprising,” “having,” “containing,” “involving,” andvariations thereof is meant to encompass the items listed thereafter andequivalents thereof as well as additional items. References to “or” maybe construed as inclusive so that any terms described using “or” mayindicate any of a single, more than one, and all of the described terms.Any references to front and back, left and right, top and bottom, upperand lower, and vertical and horizontal are intended for convenience ofdescription, not to limit the present systems and methods or theircomponents to any one positional or spatial orientation. Accordingly,the foregoing description and drawings are by way of example only.

What is claimed is:
 1. A piezoelectric material comprising: AlN dopedwith cations of one or more elements selected from the group consistingof: a) one of Sb, or Nb; b) Cr in combination with one or more of B, Sc,Y, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, or Yb; c) one of Nb and Ta incombination with one of Li, Ca, Ni, or Co; or d) one or more of Co, Sb,Ta, Nb, Si, or Ge in combination with one or more of Sm, Eu, Gd, Tb, Dy,Ho, Er, Tm, or Yb; the cations at least partially substituting for Al ina crystal structure of the piezoelectric material.
 2. A piezoelectricmaterial having the formula Al_(1-5/3x)Ta⁵⁺ _(x□2/3x)N 0<x<0.25, □representing a vacancy in an Al site in the crystal structure of thepiezoelectric material.
 3. A piezoelectric material comprising AlN dopedwith cations of Cr in combination with B and having the formulaAl_(1-2x)B_(x)Cr_(x)N 0<x<0.15, the cations at least partiallysubstituting for Al in a crystal structure of the piezoelectricmaterial.
 4. A piezoelectric material comprising AlN doped with cationsof Cr in combination with one or more of Sc, Y, Sm, Eu, Gd, Tb, Dy, Ho,Er, Tm, or Yb and having the formula Al_(1-x-y)Cr³⁺ _(x)M^(III) _(y)N,where M^(III)=Sc³⁺, Y³⁺, or Sm³⁺ . . . Yb³⁺, and where Sm³⁺ . . .Yb³⁺=any one or more of the Lanthanides with atomic numbers from 62-70,the cations at least partially substituting for Al in a crystalstructure of the piezoelectric material.
 5. The piezoelectric materialof claim 1 having a Wurtzite crystal structure.
 6. An acoustic waveresonator including the piezoelectric material of claim
 1. 7. Theacoustic wave resonator of claim 6 configured as a solidly mountedresonator.
 8. The acoustic wave resonator of claim 6 configured as afilm bulk acoustic resonator.
 9. A filter including the acoustic waveresonator of claim
 6. 10. The filter of claim 9 having a passband in theradio frequency band.
 11. An electronic device module including thefilter of claim
 9. 12. An electronic device including the electronicdevice module of claim
 11. 13. The electronic device of claim 12 whereinthe electronic device module is a radio frequency electronic devicemodule.
 14. An acoustic wave resonator including the piezoelectricmaterial of claim
 3. 15. A filter including the acoustic wave resonatorof claim
 14. 16. An electronic device module including the filter ofclaim
 15. 17. An electronic device including the electronic devicemodule of claim
 16. 18. An acoustic wave resonator including thepiezoelectric material of claim
 4. 19. A filter including the acousticwave resonator of claim
 18. 20. An electronic device module includingthe filter of claim 19.